As far as the best airport, it depends where you are flying from. If you don't live in Texas, you will need to fly into Houston Bush International Airport; fares are usually lower than they are to Houston Hobby.
Some cruise lines offer shuttles to and from the airport, others don't - at least not if you don't buy your flights through the cruise line. You didn't specify which cruise line you are using.
If you booked through a travel agent, ask her/him to check on this for you, as TA's are used to coordinating all aspects of a trip.